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Articles

Solvability of a pseudodifferential linear complementarity problem related to a viscoelastodynamic contact model

Pages 1372-1384 | Received 07 Jun 2017, Accepted 02 Sep 2017, Published online: 20 Sep 2017

References

  • Signorini A. Sopra alcune questioni di statica dei sistemi continui. Ann Scuola Norm Sup Pisa Cl Sci. 1933;2(2):231–251.
  • Kim JU. A boundary thin obstacle problem for a wave equation. Commun Partial Differ Equa. 1989;14(8–9):1011–1026.
  • Eck Ch, Jarušek J, Krbec M. Unilateral contact problems. Variational methods and existence theorems. Boca Raton: Chapman & Hall/CRC; 2005.
  • Schatzman M. A hyperbolic problem of second order with unilateral constraints: the vibrating string with concave obstacle. J Math Anal Appl. 1980;73(1):138–191.
  • Dabaghi F, Petrov A, Pousin J, et al. Convergence of mass redistribution method for the wave equation with a unilateral constraint at the boundary. ESAIM Math Model Numer Anal. 2013;48(4):1147–1169.
  • Amerio L, Prouse G. Errata corrige: “study of the motion of a string vibrating against an obstacle”. Rend Mat (6). 1975;8(2):563–585; Rend Mat (6). 1975;8(3):843.
  • Amerio L. On the motion of a string vibrating through a moving ring with a continuously variable diameter. Atti Accad Naz Lincei Rend Cl Sci Fis Mat Nat (8). 1977;62(2):134–142.
  • Amerio L. A unilateral problem for a nonlinear vibrating string equation. Atti Accad Naz Lincei Rend Cl Sci Fis Mat Nat (8). 1978;64(1):8–21.
  • Schatzman M. Un problème hyperbolique du second ordre avec contrainte unilatérale: la corde vibrante avec obstacle ponctuel. J Differ Equ (2). 1980;36(2):295–334.
  • Citrini C. The motion of a vibrating string in the presence of a point-shaped obstacle. Rend Sem Mat Fis Milano. 1985;52(353–362):1982.
  • Citrini C, Marchionna C. On the problem of the point shaped obstacle for the vibrating string equation cmy = f(x, t, y, yx, yc). Rend Accad Naz Sci XL Mem Mat. 1981;5:53–72.
  • Lebeau G, Schatzman M. A wave problem in a half-space with unilateral conditions at the boundary. J Differ Equ. 1984;53:309–361.
  • Jarušek J, Málek J, Nečas J, et al. Variational inequality for a viscous drum vibrating in the presence of an obstacle. Rend Math. 1992;12(8–9):943–958.
  • Jarušek J. Dynamic contact problems with given friction for viscoelastic bodies. Czechoslovak Math J. 1996;46(121):475–487.
  • Petrov A, Schatzman M. Mathematical results on existence for viscoelastodynamic problems with unilateral constraints. SIAM J Math Anal. 2009;40(5):1882–1904.
  • Kuttler KL, Shillor M. Regularity of solutions to a dynamic frictionless contact problem with normal compliance. Nonlinear Anal. 2004;54:1063–1075.
  • Martins JAC, Oden JT. Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Nonlinear Anal Theory Meth Appl. 1987;11(3):407–428.
  • Kuttler KL, Shillor M. Dynamic contact with Signorini’s condition and slip rate dependent friction. Electron J Differ Equ. 2004;83:1–21.
  • Dautray R, Lions J-L. Mathematical analysis and numerical methods for science and technology. Vol. 3. Berlin: Springer-Verlag; 1990.

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